1

Evaluation of seismic behavior of masonry building materials

by using a plastic failure model

. 3 L.Shahriari ،2 Safi M. ، 1.*,A.h.baziar

1- Department of civil Engineering, Islamic Azad University, Bushehr Branch, Bushehr,

Iran

2 - Department of civil Engineering,shahid Beheshti University, Shahid Abbaspoor

Campus ,Tehran, Iran.

3 - Department of civil Engineering, Islamic Azad University,Shiraz Branch,Shiraz,

Iran

Abstract

In general, most of the buildings in rural areas possess masonry structures, and generally

this kind of structure is vulnerable against the earthquake with a poor performance. So,

studying and understanding these structures in any region due to climate and the relative

risk based on the principle of earthquake strengthening and the possibility of basic securing

the buildings is inevitable for removing the weaknesses. Using the model of plastic failure

behavior of concrete materials, which are available in Abaqus finite element software, we

studied the behavior of buildings structures as their principals are different from the theory

of micro and macro models.

One of the main Paradoxes is about the access to structural failure output (cracking) which

is not available in other behavioral models. This research has Numerical studies and

models are studied by using Abaqus software which then subjected to pushover analysis.

Since then the seismic analysis are taken and results of software analysis are examined

after extraction from ABAQUS software.

Items extracted from Abaqus software included of stresses in two directions of X and

Y, cracks in structures, kinetic energies, accessible strain and the stress. Finally, a three-

dimensional seismic analysis of structure was performed by the software and the

destruction of buildings was also monitored Keyword: Continuous model, building materials, finite element method, plastics failure

* Corresponding author: amirhossein baziar Email: amir.hb@chmail.ir

2

Introduction

Non-reinforced building structures are types of buildings in which all or some parts of the

vertical and lateral loads are tolerated by walls of masonry materials generally of brick,

brick, concrete block or stone. Construction of building with building materials such as

brick or adobe building causes heavy losses during the medium earthquakes. Therefore,

improper effects of building materials used in the construction of buildings are obvious to

everyone. But for economic reasons, ease of production and construction, good insulation

properties and viewing, causes the application of these materials in buildings especially in

the rural areas.

Regarding the seismic history of Iran, it was shown that rural buildings exposed to

earthquakes with a magnitude of 5.5 or more on the Richter scale have been fully or major

damaged [2]. This type of structure does not meet the terms and conditions for seismic

stability and as long as the required changes are not implemented, we often observe the

painful events similar to those occurred in Manjil and Roodbar. In general, taking a look at

the history of earthquakes in the country, it is clear that rural homes located in the central

zone of earthquakes with a magnitude of more than 5.5 Richter, are in the risk of cracking

and collapsing.

Of course, the urban brick buildings arranged with cement mortar are more resistant and

may be more stable against earthquakes with a magnitude of 6 to 6.5 Richter. But for most

of non-reinforced brick buildings with it is not possible to tolerate earthquakes with a

magnitude of 7 or more, and such buildings collapse in the earthquake. Without a doubt,

enhancing the quality of materials and method of construction, the integrity of the roof and

lightening, as well as embedding the elements which increase the softness of buildings)

such as horizontal coils (which can increase the strength of the building) but none of the

definitive measures does not guarantee the definite stability of the structure against

earthquakes [3].

Reviewing the previous researches

Construction of building with masonry materials such as stone was widespread since the

beginning of the twentieth century where the new building materials such as concrete and

steel were used instead, for buildings with low to medium height. Given that these

buildings experience heavy losses even in average time of the earthquake, therefore, the

inappropriate materials for use in construction of building became obvious to everyone [2].

Some studies have been conducted in Iran and other countries about the reinforcement of

buildings with materials, as shown below:

Silva and colleagues in 2010 studied the behavior of the inter-plate behavior of three layers

stone walls and divided their research to two sections of assessment and evaluation of the behavior of simple wall and evaluation of the walls reinforced with grout injection

(Figure 1). In general, the main purpose of their study was to determine the response of

three layers reinforced stone walls to grout injection method. The findings are as follows:

In the case of the walls under high vertical overhead that injection grout was not

implemented in them, the cause of final failure was ultimate shear failure, while rocking

mechanism was observed for the injected walls.

3

Figure 1. Stone masonry wall used by Senthivel and Lourenco in the laboratory and numerical model [7]

The main weakness of masonry buildings against earthquake is not the lack of strength, but it is the lack of plasticity (ductility). When a composite frame is put under

lateral force on its plate, separation occurs between the frame and cross-frame in the

tension corners and a crack is form known as “border crack”. By increasing the force, the

diagonal cracks are formed along the pressure diameter, as by developing to the cross-

frame, the force is as high as the stresses occurred in the compressive corners crush the

cross-frame and failure is happened. After corner failure, the hardness is extremely reduced

but is not zero. Gradually, the final failure occurs by loading which can be known as the

completely plastic area (Figure 2).

Figure 2. Graph of force-displacement [4]

3- Evaluating the results of finite element analysis software Generally there are three ways to define the behavior of nonlinear materials. These three

methods are included of distinct model, micro model and macro model. Application of the

first two methods is not computationally effective. Therefore the macro model is used

4

which can be applied in Abaqus software for continuous models such as masonry and

concrete materials using three models of cracks in the concrete, brittle crack model, plastic

hybrid model, that since the model of brittle cracks can be applied in implicit method and

due to non-linear and brittle concrete,

this method is flawed , and the brittle crack model is weak in simulation of cyclic behavior

that does not consider the crushing of masonry materials, therefore since the plastic hybrid

approach can be applied both in explicit and implicit ways, it has a good ability to conduct

simulations. This model has the overall capability for modeling of concrete and other

quasi-brittle materials in all types of structures. That is why this model has been used. In

Plastic hybrid model of concrete damage, it was assumed that the uniaxial compressive and

tensile response of concrete is as shown in Figure 12.3.

Obviously, the stress-strain response under uniaxial tension shows a linear elastic behavior

up to failure stress of σ t0 (Figure 3 (a)). The fracture stress corresponds to the nucleation of

micro-cracks in the concrete material. It was also observed that stress-strain response under

uniaxial pressure is linear up to the initial linear yield stress of σ t0. Figure (3-b) [5].

The energy required to open the unit era of crack (Gf) was introduced by Hilerburg in

1976, as the property of matter using concepts of failure of brittle materials. Using this

method, concrete brittle behavior is specified by response of stress-displacement instead of

stress-strain. Failure energy of cracking model can be presented by Postfailure stress as a

function of displacement caused by cracking, as shown in Figure 4a. In this case, the

failure stress (σ t0) is defined as a function of the fracture energy.

In this case, it is assumed that the strength of the concrete member after cracking is

decreased linearly as shown in Figure 4b. In reality, cracking displacement is happened

when the strength is completely faded. In this case, the cracking value is as: )/

σ t0

(a) At tension [26]

b) at compression [26]

Figure 3- Concrete responding to the uni-axial loading [26]

5

a) Failure energy at tension [1]

b) Failure energy at compression [1]

Figure 4- Failure energy of masonry and building materials

In Abaqus software, the materials non-decreasing local quantities of variables are considered, so the damage factor of the concrete is shown as below:

)1(

Where dt is the tensile damage factor (a. number between 0-1, as zero shows the non-

damaged material and 1 represents the completely damaged one). Shows the tensile

equivalent plastic strain. Potential of the plastic flow (G) for this model is the Drucker-

Prager hyperbolic function as shown by Eq.2.

(2)

Where the hydrostatic compressive stress is defined based on the invariables of the

effective stress as shown in eq.3

(3)

Where is the matrix of the invariables of the effective stress, obtained by eq.4

(4)

Where is the first elasticity matrix (not damaged) of concrete. It should also be noted

that in eq.6.3 the effective stress is equivalent to Mizes expressed by Eq.5.

(5)

Where is the effective stress of the diversion obtained by Eq.6

(6) In addition, φ is the dilation angle measured at p-q plate and σ t0 is the uni-axial tensile

stress of failure and ε is the Eccentricity-dependent parameter denoting the rate of

approximation of potential flow to the Asymptote. Of course, it should be noted that when

the Eccentricity moves toward zero, flow potential shifts to a straight line [6].

In the behavioral model of yield function, the yield function is used to calculate the

evolutionary trend of strength under stress and pressure as the evolutionary of the surface

6

is controlled by variables of and . The yield function based on the effective stresses

is s shown below:

(7)

In Eq.7, is the main effective stress and parameters of ɑ, β and ϒ are calculated based on Eq.8 to Eq.10.

(8)

(9)

(10)

Where is the ratio of initial equibiaxial compressive yield stress to the uniaxial initial

compressive stress, as the default value was set 1.16. In addition, is the tensile

strength and value of is obtained by Eq.11 [7].

(11) Where E0 is the initial elastic strength (non-damaged materials) and dt is the parameter of

the tensile damage. Also is the effective compressive stress and value of is

calculated using Eq. 16.2.

(12)

Where dc parameter is the compressive damage of the material usually a number between

0-1. Also it should be noted that Kc shows the ratio of concrete tensile and compress

invariables, set as 2.3 as default 4. Investigating the accuracy of results obtained by ABAQUS software analysis

In order to verify the accuracy of modeling and solving method in ABAQUS software, a

laboratory model was used derived in 1995 by Vitorion named "numerical and

experimental study of building walls under cyclic loading with mechanical properties and

boundary conditions, and similar loading”. It was made and analyzed by software and is

applied to verify the results of numerical modeling with experimental results in this study.

Software model is made in homogenous form model and the given mechanical

specifications of the wall are listed in Table 1.

Table 1. Characteristics of the numerical model Module of

elesticity

Poisson

coefficien

t

Dilatio

n angle

Density

of

material

s

Overloa

d force

Compressive

behavior

Tensile behavior

382500000

0

0.2 56ᵒ 1800

Kg/m3

100KN

1

Inelasti

c strain

Yield

stress

Crackin

g strain

Yield

stress

100KN

2

0.0014

1

297656.2

5

0.00057 2958

0

7

Mechanism o failure of laboratory wall at the end of loading under overload of 100KN and

lateral force is shown in Figure 5. However, the plastic damages of walls after finite

element analysis can be seen in Figure 6. Software could detect faults and cracks in the

walls as well. On the other hand, the force- displacement curve obtained by laboratory

work of Vitorion and software modeled diagram is shown in Figure 7. Obviously, no

significant difference can be seen in the detection of capacity of the wall and, therefore,

modeling and testing in laboratory do not differ from each other and are well approximated

(Figure 7).

Figure 5. An image of the wall constructed in the

laboratory after loading [9].

Figure 6. An image of the wall constructed in the software

after loading (diagonal compressive cracks of wall)

Laboratory [9]

abaques

Figure 7. c. The force-displacement graph of control sample compared to the results obtained by ABAQUS

8

5. Numerical models derived by the software In general, today there are two methods among researchers to model the wall;

macro modeling; in this way the whole set wall is considered as a homogeneous body

and for the intended homogeneous body, all mechanical properties such as modulus of

elasticity intended all, yield stress and strain and final strain are imported to the

software by standard special test.

The micro modeling; in this case, wall materials are defined individually, as for each of

them mechanical properties and relevant behavior is imported to software. Application

of this method is much more complicated than the previous method and the time it

takes to finite element analysis in this way is so much longer than macro model.

Therefore the macro modeling approach is used.

5.1. Characteristics of material and dimensions of the wall modeled in

the software The modeled Wall was considered with a thickness of 20 cm length of 3.5m and height of

2.7 meters without openings as a concrete bundle was located on it. The mentioned wall

was a bearing wall as the 200KN gravity load was widely places on the on coils over the

wall. It was clamped at the top and down sides under a simultaneous lateral loading. The

maximum compressive and tensile strains were max 0.005 and 0.22, respectively.

Elements used in the mesh was C3D8R for walls and concrete beams, S4R for the bed,

C3DR8 for three-dimensional ceiling (Figure 8). The purpose of this model was to detect

the cargo and cracking model of a simple wall. In addition, a building with all its openings

under seismic load was simulated by software, as the size of the investment plan and

perspective is shown in Figure 9. Figure 10 also shows the model meshed model of this

building.

Figure 8. A continues simple wall with meshed configuration

9

Figure 9. sample of a 3D model of a building simulated in the software (Values are in

meter)

Figure 10. Meshing of the building structure modeled in the software

5.2. Choosing the accelerograms of earthquakes in numerical analysis

Selected earthquakes have been extracted from seismic bank of strong motion in PEER

Land Bank. Selected earthquake was happened on the Soil type III (such as old Bushehr

texture). Since for the region with relatively high risk, based on the standard 2800, the

PGA value was equal to 0.3g. The chosen PGA earthquake was about 0.3g to meet the

dependency effects of earthquake frequency to PGA. The napalm earthquake was occurred

during 5.32sec at a distance of 10 kilometers from the source with the magnitude of 6

Richter. The earthquake occurred in 1986.07.08. Figure 8 shows the quake's horizontal

component.

10

Figure 8. Horizontal acceleration component of napalm earthquake

6. Results of analysis First, in one step the overload force of 100 kN was applied to simple wall and after the

analysis of stresses and deformations, the lateral force was applied to the wall as

displacement and the value of imposed force and deformation were calculated at the end.

Finally diagram of force-displacement were drawn based on the two parameters.

Accordingly, the maximum shift in the end of analysis was 2.5 cm and a maximum shear

stress was predicted to be 0.62 MPa (Figure 11). In addition the ultimate behavior of wall

under a basic shear graph (force-displacement) was shown in Figure 13. The border crack

of structure was occurred after 5mm and diagonal cracks were also developed followed by

increase of displacement as about 1cm.

Figure 11. Contour of simple displacement

(in meter)

Figure 12. Contour of shear stresses

created in simple wall (in Pascal)

11

Figure 13. Graph of force-displacement of a simple wall

6.1. Studying the Seismic Response of three-dimensional building

modeled by using continuous model In this section, behavior of the walls of the three-dimensional buildings is described and it

will be examined in the case of the tension on the wall affected by Earthquake. In this

regard, Figures 14, 15 and 16 described the stress contours in 1, 3.67 and 5.45seconds after

the Earthquake. In moments of 1 and 3.67 seconds, the value of obtained stress was more

than compressive stress which can be tolerated by the walls. The amount of stress are 2.67

and 1.53 MPa (Figure 14 and 15).

The tensions are gradually reduce and Earthquake velocity decreases, as at the times of

5.45 seconds, it reached 1.32 MPa (Figure 16). It should be noted that Tolerable

compressive stress in building stone walls was considered about 1 MPa in the software.

Although regarding the contours shown in early times, the wall showed an elastic behavior

in most areas, but at the initial seconds, nonlinear performance of wall in lots of areas such

as boundaries, heel and hotspots was subjected to plastic tensions. In addition to the

surrounding walls, this point is also dominant for the internal walls of the building. But the

stress value is considerably lower than the surrounding walls (Figure 17).

Figure 14 Mises stress Contour - 1 second after occurrence

Figure 15 Mises stress contour – 3.67 seconds after

occurrence

12

By observing the contours of 14 to 16, we can find out that the junction of walls and

openings margin have chosen tensions. According to Figure 10d, maximum stresses were

2.67, 1.63 and 1.52, imposed at the wall-to-wall connection points, door and window

openings margins, respectively. It is important to note that due to the acceleration peak of

earthquake was occurred at 1 to 2 seconds, the maximum stress on the same joints of wall-

to-wall moments was also occurred at these moments (Figure 17).

6.2. Investigating the status of cracking of walls

In general, most of the walls of the buildings have been damaged severely in

the direction of the horizontal component of and this important point in

Figures 18 and 19. Figure 18 shows the moment and location of diagonal

cracks in the wall. In the case of type of cracks in walls it must be stated that

the dominant failure in Iranian building structures is because of the mortar

slip and diagonal tension. As shown in Figures 19 and 20, the walls of

buildings in this case have been subjected to diagonal tensions, as the

direction of building cracks in direction of acceleration has rotated as 45

degrees in relation to the horizontal components of the earthquake. In Figure

20 all of the cracks of the building at the end of the seismic analysis are

shown.

Figure 16 Mises stress contour 5.45 seconds after

occurrence

Figure 17 History of stress changes in areas of

the connection

13

One of the most decisive factors in the improvement of existing buildings is

to determine the forces of the dynamic analysis. Figure 21 shows the history

of horizontal forces (base shear) induced by seismic causes of the building.

As shown in Figure 21, the maximum horizontal cut of the structure was

determined at the moment of 0.67 seconds after earthquake occurrence, was

89MN determined, that the figure is not illogical given the huge amount of

weight of this structure. Conclusion

In general, most of the buildings in rural areas are composed of are masonry

structures, and generally this kind of structure have a poor performance

against the Earthquake, so studying and understanding of these structures in

each region according to the climate and the relative risk of earthquake,

Figure 21- History of base shear of Building

Figure 18- The time and location of cracks in the

direction of vibrations

Figure 19- Development of cracking of walls in the direction

of vibration

Figure 20- Cracks of the building at the end of seismic analysis

14

exploring the possibility of securing buildings and fixing the weaknesses is

inevitable. However, the technique of implementation of these structures is

the same in every region of the world, but the materials used to build the

structures are different.

Usually the type of these materials (climate stones, bricks or blocks with

diverse mortars used for construction of these buildings) causes that the

accurate evaluation methods of these structures becomes a bit complicated. In

three-dimensional buildings, Mises stresses of the wall after seismic vibration

of the building were assessed in the moments of 1, 3.67 and 5.45 seconds.

The values of these tensions were 2.67, 1.53 and 1.32 MPa. It should be

explained that the mentioned building was tested by seismic analysis in its

strong direction, in which direction the inner walls failed against the seismic

vibrations, despite the weaker direction (X) as the most failure was happened

due to large openings and surrounding wall.

8. Reference

1. TAbesh Pour, M. R, Farhangfar, H., (2006), Seismic retrofitting of

masonry adobe structures, the first National Conference on Earthquake Crisis

Management in a historical context, Yazd, Yazd University.

2. Sabet, E, Kurdestani, 2012, Behavior of masonry buildings against the

earthquake and how to strengthen them, the second National Disaster

Management Conference.

3. Fiuz, A.R, Abdolkarim, P., Vaghefi, M., Jafar, P., (2013), Studying the

behavior and resistance of load-bearing of stone walls against the earthquake,

the first International Conference of Civil Engineering, Architecture and

urban development, Tabriz

4. Moghaddam, H. 2008, Seismic design of brick buildings, Tehran, Institute

of Scientific Publications of Sharif University

5. ABAQUS Documentation, Analysis User’s Manual, Version 6.14.2, 2015

6. Daniel P. Abrams & Nirav Shah, (1992), Cyclic Load Testing of

Unreinforced Masonry Walls, Advanced Construction Technology Center

Project titled NDE of Masonry Building.

7. Senthivel, R, Lourenço, B, (2009), Finite element modelling of

deformation characteristics of historical stone masonry shear walls,

Engineering Structures, Vol. 31, 1930–1943

8. Silva, B, Benetta, M, Francesca, P, Modena, C, (2010), Experimental

assessment of in-plane behaviour of three-leaf stone masonry walls,

Construction and Building Materials 53, 149–161.

9. Daniel Vitorion, Experimental and Numerical Analysis of Blocky Masonry

Structures under Cyclic Loading, Thesis submitted for Doctoral Philosophy of

Structural Engineering, MinhoUniversity, Portugal, 2010.